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Weighted Littlewood-Paley Theory and Exponential-Square Integrability

  • Michael Wilson

Part of the Lecture Notes in Mathematics book series (LNM, volume 1924)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Pages 1-7
  3. Pages 39-68
  4. Pages 145-150
  5. Pages 151-160
  6. Pages 161-188
  7. Pages 189-195
  8. Pages 213-218
  9. Back Matter
    Pages 219-228

About this book

Introduction

Littlewood-Paley theory is an essential tool of Fourier analysis, with applications and connections to PDEs, signal processing, and probability. It extends some of the benefits of orthogonality to situations where orthogonality doesn’t really make sense. It does so by letting us control certain oscillatory infinite series of functions in terms of infinite series of non-negative functions. Beginning in the 1980s, it was discovered that this control could be made much sharper than was previously suspected. The present book tries to give a gentle, well-motivated introduction to those discoveries, the methods behind them, their consequences, and some of their applications.

Keywords

Singular integral Square function exponential-square maximal function weighted inequality

Authors and affiliations

  • Michael Wilson
    • 1
  1. 1.Department of MathematicsUniversity of VermontBurlingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-74587-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-74582-2
  • Online ISBN 978-3-540-74587-7
  • Series Print ISSN 0075-8434
  • Buy this book on publisher's site